Nearly 6,800 frontline police jobs have gone since the 2010 general election as a result of spending cuts, according to a House of Commons analysis of updated Home Office figures.

Her Majesty's Inspector of Constabulary (HMIC) predicted in July that 5,800 frontline jobs would be lost over the entire five-year parliament, and ministers have repeatedly urged police chiefs to make deeper cuts in their "middle and back office" staff to protect the national frontline.

The figures show there has been an average 6% reduction in frontline policing across England and Wales. But eight forces have lost over 10% of their of their frontline officers, including 16% in Warwickshire and 13% in Nottinghamshire. Only two out of the 43 forces have fulfilled ministerial hopes of using the 20% budget cuts to boost their frontlines through reorganisation.

The disclosure comes as the Electoral Commission reveals that it is to spend £3.69m on an advertising campaign, and sending booklets to the 21 million households in England and Wales outside London amidst dire predictions that turnout in the first police and crime commissioner elections in November could fall below 20%. A separate £3m Home Office television, radio and press campaign starts next month.

The shadow home secretary, Yvette Cooper, who commissioned the research into the impact of the cuts, said the analysis showed their impact had been faster and deeper than expected. "Police and crime commissioners will be put in an impossible position," she said.

The 41 elected police and crime commissioners will be legally required to approve budgets, and will be left with little, if any, room for manouevre to reverse funding cuts. The home secretary can order a local referendum if any commissioner insists on an "excessive" increase in the police precept on council tax payers.

"Six thousand eight hundred frontline officers have gone in two years compared to the 5,800 that Her Majesty's Inspectorate predicted would be lost over five years. Given the concern over community safety it is no wonder the government is looking for someone else to blame," said Cooper.

"Holding the elections for police and crime commissioners in November is more expensive too, costing over £100m when that money could have kept more officers in post.

"We know Theresa May will try to hide behind PCCs as communities deal with the serious consequences of [losing] so many officers from our high streets and community beats.

"Yet it is government decisions which are undermining the ability of the police to fight crime."

A Home Office spokesman said the HMIC's original predictions were based on exhaustive work with police forces and covered the period up to 2015: "They show that the proportion of officers on the frontline will rise. The vast majority of forces are rising to the challenge we set them of improving services while making their contribution to reducing the deficit. Crime is down, victim satisfaction is improving and the response to emergency calls is being maintained," he added.